Papers by Mohammad Dilshad
Mathematics
A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduc... more A new generalized Yosida inclusion problem, involving A-relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q-uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra–Fredholm integral equation is examined.
Fractal and Fractional
In this paper, we design two inertial iterative methods involving one and two inertial steps for ... more In this paper, we design two inertial iterative methods involving one and two inertial steps for investigating a general quasi-variational inequality in a real Hilbert space. We establish an existence result and a non-trivial example is furnished to substantiate our theoretical findings. We discuss the convergence of the inertial iterative algorithms to approximate the solution of a general quasi-variational inequality. Finally, we apply an inertial iterative scheme with two inertial steps to investigate a delay differential equation. The results presented herein can be seen as substantial generalizations of some known results.
AIMS Mathematics
In this article, we suggest and analyze the splitting type viscosity methods for inclusion and fi... more In this article, we suggest and analyze the splitting type viscosity methods for inclusion and fixed point problem of a nonexpansive mapping in the setting of Hadamard manifolds. We derive the convergence of sequences generated by the proposed iterative methods under some suitable assumptions. Several special cases of the proposed iterative methods are also discussed. Finally, some applications to solve the variational inequality, optimization and fixed point problems are given on Hadamard manifolds.
Journal of Inequalities and Applications
This article aims to introduce and analyze the viscosity method for hierarchical variational ineq... more This article aims to introduce and analyze the viscosity method for hierarchical variational inequalities involving aϕ-contraction mapping defined over a common solution set of variational inclusion and fixed points of a nonexpansive mapping on Hadamard manifolds. Several consequences of the composed method and its convergence theorem are presented. The convergence results of this article generalize and extend some existing results from Hilbert/Banach spaces and from Hadamard manifolds. We also present an application to a nonsmooth optimization problem. Finally, we clarify the convergence analysis of the proposed method by some computational numerical experiments in Hadamard manifold.
Mathematics
In this paper, we alter Wang’s new iterative method as well as apply it to find the common soluti... more In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem (SpVIP) in Hilbert space. We discuss the weak convergence for (SpVIP) and strong convergence for the common solution of (SpVIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes.
Journal of function spaces, Mar 29, 2022
is study aims at investigation of a generalized variational inequality problem. We initiate a new... more is study aims at investigation of a generalized variational inequality problem. We initiate a new iterative algorithm and examine its convergence analysis. Using this newly proposed iterative method, we estimate the common solution of generalized variational inequality problem and fixed points of a nonexpansive mapping. A numerical example is illustrated to verify our existence result. Further, we demonstrate that the considered iterative algorithm converges with faster rate than normal S-iterative scheme. Furthermore, we apply our proposed iterative algorithm to estimate the solution of a convex minimization problem and a split feasibility problem.
An Iterative Algorithm for a Common Solution of a Split Variational Inclusion Problem and Fixed Point Problem for Non-expansive Semigroup Mappings
Industrial Mathematics and Complex Systems, 2017
In this paper, we consider a split variational inclusion problem and a fixed point problem for no... more In this paper, we consider a split variational inclusion problem and a fixed point problem for non-expansive semigroup mappings in real Hilbert spaces. An iterative algorithm is introduced to approximate the common solution of split variational inclusion problem and a fixed point for a non-expansive semigroup mappings. Further, under some suitable conditions, it is proved that the sequences generated by the proposed algorithm converge strongly to a common solution of split variational inclusion problem and fixed point problem for a non-expansive semigroup mappings.
Journal of Function Spaces, 2022
In this paper, we present two iterative algorithms involving Yosida approximation operators for s... more In this paper, we present two iterative algorithms involving Yosida approximation operators for split monotone variational inclusion problems ( S p MVIP ). We prove the weak and strong convergence of the proposed iterative algorithms to the solution of S p MVIP in real Hilbert spaces. Our algorithms are based on Yosida approximation operators of monotone mappings such that the step size does not require the precalculation of the operator norm. To show the reliability and accuracy of the proposed algorithms, a numerical example is also constructed.
Iranian Journal of Fuzzy Systems, 2012
In this paper, we introduce and study a mixed variational inclusion problem involving innite fami... more In this paper, we introduce and study a mixed variational inclusion problem involving innite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving innite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.
Journal of Mathematical Inequalities, 2020
The purpose of this paper is to present iterative methods to solve a split common null point prob... more The purpose of this paper is to present iterative methods to solve a split common null point problem in real Hilbert spaces such that the implementation of proposed iterative schemes do not require any pre-existing estimation of the norm of bounded linear operator. We give the weak and strong convergence of the proposed algorithms under some mild and standard assumptions in Hilbert spaces. A numerical example is also constructed to illustrate the algorithm for strong convergence.
In this paper, we pose a new iterative algorithm and show that this newly constructed algorithm c... more In this paper, we pose a new iterative algorithm and show that this newly constructed algorithm converges faster than some existing iterative algorithms. We validate our claim by an illustrative example. Also, we discuss the convergence of our algorithm to approximate the solution of a general variational inclusion problem. Also, we present a numerical example to verify our existence and convergence result. Finally, we apply our proposed iterative algorithm to solve a delay differential equation as an application
Symmetry, 2021
This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion pro... more This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·,·)-compression XOR-αM-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.
Journal of Function Spaces, 2021
In this article, we consider and study a system of generalized set-valued variational inequalitie... more In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.
Computational and Applied Mathematics, 2020
In an attractive article, Rahman et al. introduced the split monotone Yosida variational inclusio... more In an attractive article, Rahman et al. introduced the split monotone Yosida variational inclusions (SMYVI) and estimate the approximate solution of the split monotone Yosida variational inclusions using nonexpansive property of operators. The main result of this paper has flaw and not correct in the present form. We modify the SMYVI and give the strong convergence theorem under some new assumptions. We also give a weak convergence theorem to solve modified split Yosida variational inclusion problem using properties of averaged operators with three new supporting lemmas. Keywords Split monotone Yosida variational inclusions • Inverse strongly monotone operator • Averaged operator • Nonexpansive operator Mathematics Subject Classification 47H05 • 47H09 • 47J25 Communicated by Baisheng Yan.
Journal of Function Spaces, 2020
This article is aimed at introducing an iterative scheme to approximate the common solution of sp... more This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.
Journal of Nonlinear Sciences and Applications, 2012
In this paper, we define H(•, •)-η-cocoercive operators in q-uniformly smooth Banach spaces and i... more In this paper, we define H(•, •)-η-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent operator. We prove the Lipschitz continuity of the resolvent operator associated with H(•, •)-η-cocoercive operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved. Some examples are given.
Generalized Monotone Mappings with Applications
Industrial and Applied Mathematics, 2015
In this work, we introduce a generalized monotone mapping and we call it H(∙,∙)-cocoercive mappin... more In this work, we introduce a generalized monotone mapping and we call it H(∙,∙)-cocoercive mapping. Then, we have extended this concept of H(∙,∙)-cocoercive mapping to H(∙,∙)-η-cocoercive mapping. Further, we have proved some of the properties of H(∙,∙)-cocoercive and H(∙,∙)-η-cocoercive mappings and finally apply these concepts to solve some generalized variational inclusions and system of variational inclusions.
In this paper, we study an existence theorem of solutions for generalized quasi-variational-like ... more In this paper, we study an existence theorem of solutions for generalized quasi-variational-like inclusions involving (A, η) and relaxed cocoercive mappings. We have shown that the approximate solutions obtained by proposed algorithm converge to the exact solutions of generalized quasi-variational-like inclusions. As an application, we have shown that generalized quasi-variational-like inclusions include optimization problems and also an equivalence with A-resolvent equations is given.
American Journal of Operations Research, 2011
In this paper, we generalize , H -accretive operator introduced by Zou and Huang [1] and w... more In this paper, we generalize , H -accretive operator introduced by Zou and Huang [1] and we call it , H ---accretive operator. We define the resolvent operator associated with , H ---accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of , H ---accretive operator.
Application of H (·,·)-Cocoercive Operators for Solving a Set-Valued Variational Inclusion Problem Via a Resolvent Equation Problem
Indian Journal of Industrial and Applied Mathematics, 2013
ABSTRACT In this paper, we apply H(·, ·)-cocoercive operators for solving a system of variational... more ABSTRACT In this paper, we apply H(·, ·)-cocoercive operators for solving a system of variational inclusions. By using the resolvent operator technique associ-ated with H(·, ·)-cocoercive operators, we define an iterative algorithm for solving a system of variational inclusions. Convergence criteria is also discussed. Some examples are given in support the definition of H(·, ·)-cocoercive operators.
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Papers by Mohammad Dilshad