The main purpose of this paper is to show that the Meir–Keeler contraction principle, as well as ... more The main purpose of this paper is to show that the Meir–Keeler contraction principle, as well as some of its generalizations, is, in general, not true in quasi-metric spaces. After that, we suggest a new Meir–Keeler type contraction that guaranties the existence and uniqueness of fixed points in quasi-metric spaces. Finally, to illustrate the wide usability of our findings, we discuss the existence and uniqueness of solutions for an integro-differential equation in Musielak–Orlicz spaces.
Background/Objectives: In this paper, we introduced the concept of aP f,g integral contractive ma... more Background/Objectives: In this paper, we introduced the concept of aP f,g integral contractive mappings, which is a new class of integral contractive mappings and using this notion we establish a new fixed point theorem. Findings: Our paper represents a generalization and extension of fixed point theorems for mappings satisfying contractive conditions of integral type where the contractive inequality depends on rational and irrational expression. In particular, we omitted the condition of continuity (which is a very strong condition and appear in almost all papers using contractive mapping of rational type) from many existing results. Application/Improvements: As a direct consequence, some new results of integral type for rational and irrational contraction maps are presented to illustrate our obtained result.
This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation w... more This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and ψ -Caputo fractional derivative.
In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem... more In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.
International Journal of Stochastic Analysis, 2010
This paper is devoted to prove, in a nonclassical function space, the weak solvability of parabol... more This paper is devoted to prove, in a nonclassical function space, the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.
The purpose of this paper is to obtain a sufficient condition for a G-Cauchy sequence to be an M-... more The purpose of this paper is to obtain a sufficient condition for a G-Cauchy sequence to be an M-Cauchy sequence in fuzzy metric spaces. Our main result provides a partial answer to the open question posed by V. Gregori and A. Sapena. For application, we give a new fuzzy version of the Banach fixed point theorem.
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Papers by Rachid Mechri