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A Course In Functional Analysis

Functional equations in several variables

Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.

Fixed Point Theory and Applications

In this paper, we study a diffusion model of Kirchhoff-type driven by a nonlocal integro-differential operator. As a particular case, we consider the following diffusion problem where [u] s is the Gagliardo seminorm of u, is a bounded domain with Lipschitz boundary, is the fractional Laplacian with , is the initial function, and is continuous. Under some appropriate conditions, the local existence of nonnegative solutions is obtained by employing the Galerkin method. Then, by virtue of a differential inequality technique, we prove that the local nonnegative solutions blow-up in finite time with arbitrary negative initial energy and suitable initial values. Moreover, we give an estimate for the lower and upper bounds of the blow-up time. The main novelty is that our results cover the degenerate case, that is, the coefficient of could be zero at the origin.

Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions

Coincidence point theorems in probabilistic and fuzzy metric spaces

On the stability of J∗-derivations

We introduce two reasonable versions of approximately additive
functions in a Serstnev probabilistic normed space endowed
with Π 𝑀 triangle function. More precisely, we show under
some suitable conditions that an approximately additive function
can be approximated by an additive mapping in above mentioned 
spaces.

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Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces

Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source

In this paper, an extension of Darbo fixed point theorem is introduced. By applying our extension, we obtain a coupled fixed point theorem and a solution for an integral equation. The proofs of our results are based on the technique of measure of noncompactness.

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An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations.

In this paper, we investigate the generalized Hyres–Ulam–Rassias stability and Bourgin-type superstability of higher derivations in non-Archimedean Banach algebras by using a version of fixed-point theorem.

Mohammad Bagher Ghaemi

Papers

On the stability of J∗-derivations

Generalized Hyers-Ulam-Rassias Theorem in Menger Probabilistic Normed Spaces

Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source

An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations.

A fixed-point method for perturbation of higher ring derivations in non-archimedean banach algebras