Papers by satish shukla Shukla
Journal of Inequalities and Applications
In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and pr... more In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided.
Boundary Value Problems, May 31, 2023
In this paper, we establish a relation-theoretic set-valued version of the fixed point result ofĆ... more In this paper, we establish a relation-theoretic set-valued version of the fixed point result ofĆirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143-147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fixed point results ofĆirić and Prešić (Acta Math. Univ. Comen.
International Journal of Mathematical Archive, 2011
The object of this paper is to generalize the Fixed Point theorems in the partial cone metric spa... more The object of this paper is to generalize the Fixed Point theorems in the partial cone metric spaces given by Sönmez [1] using the concept of normality of cone. Results proved in this paper are generalization of Fixed Point results established for metric spaces.
DOAJ (DOAJ: Directory of Open Access Journals), Dec 1, 2016
In this paper, the notion of G-(F, τ)-contractions in the context of partial rectangular metric s... more In this paper, the notion of G-(F, τ)-contractions in the context of partial rectangular metric spaces endowed with a graph is introduced. Some fixed point theorems for G-(F, τ)-contractions are also proved. The results of this paper generalize, extend, and unify some known results. Some examples are provided to illustrate the results proved herein.
TWMS Journal of applied and engineering mathematics, Jun 22, 2016
In this paper, the notion of G-(F, τ)-contractions in the context of partial rectangular metric s... more In this paper, the notion of G-(F, τ)-contractions in the context of partial rectangular metric spaces endowed with a graph is introduced. Some fixed point theorems for G-(F, τ)-contractions are also proved. The results of this paper generalize, extend, and unify some known results. Some examples are provided to illustrate the results proved herein.
International Journal of Analysis and Applications, Nov 3, 2015
In this paper, we introduce the α-admissible mappings in the setting of cone metric spaces equipp... more In this paper, we introduce the α-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.
In this paper, we introduce the generalized cyclic contractions on θcomplete partial cone metric ... more In this paper, we introduce the generalized cyclic contractions on θcomplete partial cone metric spaces and prove a fixed point result in such spaces without assuming the normality of cone. Our result generalizes some known results from metric and cone metric spaces in θ-complete cone metric spaces. For illustration examples are provided.
In this paper, we introduce the notions of ordered F-(F, h)-contraction and subcontraction in the... more In this paper, we introduce the notions of ordered F-(F, h)-contraction and subcontraction in the setting of partial metric spaces. Some fixed point theorems for ordered F-(F, h)-contraction and subcontraction in 0-f-orbitally complete partial metric spaces are proved. Our results generalize some recent results of metric and partial metric spaces into the 0-f-orbitally complete partial metric spaces. Some examples are presented which illustrate the results proved herein.
Gulf Journal of Mathematics, Sep 1, 2013
In this paper we introduce the concept of tvs-cone b-metric space over solid cone. Our results im... more In this paper we introduce the concept of tvs-cone b-metric space over solid cone. Our results improve, generalize, extend, unify, enrich and complement recent fixed point results established by H. Huang and S. Xu, M. P. Stanić et al., A. S. Cvetković et al. and M. H. Shah et al. The examples are given to illustrate the usability of our results.
Set-valued Prešić–Reich type mappings in metric spaces
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, Nov 29, 2012
The purpose of this paper is to establish some coincidence and common fixed point theorems for a ... more The purpose of this paper is to establish some coincidence and common fixed point theorems for a set-valued and a single-valued mapping satisfying Prešić–Reich type contraction conditions in metric spaces. Our results generalize and extend some known results in metric spaces. An example is included which illustrate the results.
Filomat, 2015
Let (X, d) be a metric space and T : X → X be a mapping. In this work, we introduce the mapping ζ... more Let (X, d) be a metric space and T : X → X be a mapping. In this work, we introduce the mapping ζ : [0, ∞) × [0, ∞) → R, called the simulation function and the notion of Z-contraction with respect to ζ which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx, Ty) and d(x, y). The related fixed point theorems are also proved.
Fixed Points of Generalized Kannan Type α-admissible Mappings in Cone Metric Spaces with Banach Algebra
Theory and Applications of Mathematics & Computer Science, Nov 26, 2016
In this paper, we introduce the generalized Kannan type α-admissible mappings in the setting of c... more In this paper, we introduce the generalized Kannan type α-admissible mappings in the setting of cone metric spaces equipped with Banach algebra. Our results generalize and extend the fixed point result for Kannan type mappings in metric and cone metric spaces. An example is presented which illustrates our main result.
Scientific Publications of the State University of Novi Pazar, 2016
In this paper, we introduce the notion of α-admissible mappings in the setting of cone 2-metric s... more In this paper, we introduce the notion of α-admissible mappings in the setting of cone 2-metric spaces over Banach algebras. Some existence and uniqueness results of the fixed point of an α-φ-contractive mapping in cone 2-metric spaces are proved. Some examples are provided which illustrate the results proved herein.
Fasciculi Mathematici, Jul 26, 2017
We propose a new notion of multi-valued almost (GF, δ b)-contractions involving rational terms un... more We propose a new notion of multi-valued almost (GF, δ b)-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.
Carpathian Journal of Mathematics, 2015
In this paper, the well known concept of cyclic contraction is generalized in product spaces by i... more In this paper, the well known concept of cyclic contraction is generalized in product spaces by introducing a new class of operators called cyclic-Prešić operators. A fixed point result for such operators is proved. Some examples are given to validate the results proved herein.
ISRN Computational Mathematics (Online), May 23, 2013
The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed ... more The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.
Journal of Operators, Apr 22, 2013
We generalize the result of Prešić in metric-like spaces by proving some common fixed point theor... more We generalize the result of Prešić in metric-like spaces by proving some common fixed point theorems for Prešić type mappings in metric-like spaces. An example is given which shows that the generalization is proper.
Fixed Point Theory, Jun 1, 2018
The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove ... more The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove some fixed point results of contractive mappings on complex valued fuzzy metric spaces. Some examples are presented to support the results proved herein. Our results extend various results in the existing literature.
Quaestiones Mathematicae, Mar 20, 2019
In this paper, we establish a relation-theoretic version of a famous fixed point result of Nadler... more In this paper, we establish a relation-theoretic version of a famous fixed point result of Nadler on complete metric spaces endowed with a binary relation. Our results extend and generalize the recent result of A. Alam and M. Imdad (see [1], Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17(4) (2015), 693-702) and several other fixed point results on spaces endowed with various kinds of binary relations to their multi-valued versions with weaker requirements. An application of the obtained result to the problem of existence of solution of differential inclusions is presented.
Journal of Mathematics, 2013
We prove some common fixed point theorems for-contractions in 0-complete partial metric spaces. O... more We prove some common fixed point theorems for-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.
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Papers by satish shukla Shukla