On some Mann's type iterative algorithms

AbstractFirst we present some interesting variants of Mann's method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients

Sufficient conditions to solve two systems of integral equations via fixed point results

Abstract The purpose of this paper is to study the solution of two systems of nonlinear integral equations via fixed point results in a complete dislocated b-metric space. Also the notion of graphic contractions on a closed set for two families of graph dominated multivalued mappings is introduced. Our results generalize some previous results in the existing literature

Solvability of second order linear differential equations in the sequence space n(ϕ) n(ϕ)n(\phi)

Abstract We apply the concept of measure of noncompactness to study the existence of solution of second order differential equations with initial conditions in the sequence space n(ϕ) $n(\phi)$

On Mann’s Type Method for Nonexpansive and Strongly Quasinonexpansive Mappings in Hilbert Spaces

In the setting of Hilbert spaces, we study Mann’s type method to approximate strong solutions of variational inequalities. We show that these solutions are fixed points of a nonexpansive mapping and/or a strongly quasinonexpansive mapping, depending on the coefficients involved in the algorithm

Some New Fixed Point Theorems in b-Metric Spaces with Application

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results

Fixed Point Results for Multivalued Contractive Mappings Endowed with Graphic Structure

The aim of this paper is to introduce the notion of admissible multivalued mappings and to set up fixed point results for such mappings fulfilling generalized locally Ćirić type rational-contractive conditions on a closed ball in complete dislocated b-metric space. Example and application have been given to demonstrate the novelty of our results. Our results combine, extend, and infer several comparable results in the existing literature

Multivalued Fixed Point Results for New Generalized F-Dominated Contractive Mappings on Dislocated Metric Space with Application

The purpose of this paper is to find out fixed point results for semi-α⁎-dominated multivalued mappings fulfilling a new generalized locally F-dominated multivalued contractive condition on a closed ball in complete dislocated metric space. Example and application both are given to show the novelty of our results. Our results merge, extend, and infer many results

Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations

Unification of the Fixed Point in Integral Type Metric Spaces

In metric fixed point theory, the conditions like “symmetry„ and “triangle inequality„ play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary