scholarly journals Existence of solutions of implicit integral equations via Z-contraction

2018 ◽  
Vol 34 (2) ◽  
pp. 239-246
Author(s):  
PRADIP R. PATLE ◽  
◽  
DEEPESH KUMAR PATEL ◽  
Keyword(s):  
Fixed Point ◽  
Compact Operator ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
Condensing Mapping ◽  
State Of Art

The main focus of this work is to assure that the sum of a compact operator with a Z-contraction admits a fixed point. The concept of condensing mapping (in the sense of Hausdorff non-compactness measure) is used to establish the concerned result which generalizes some of the existing state-of-art in the literature. Presented result is used to verify the actuality of solutions of implicit integral equations.

scholarly journals Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chuanxi Zhu ◽  
Wenqing Xu ◽  
Zhaoqi Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Probabilistic Metric Spaces ◽  
Contraction Mappings ◽  
Probabilistic Metric

We introduce the concepts of(H,ψ,Φ)-contraction and probabilistic(α,φ)-contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results.

scholarly journals Krasnosel’skii Type Hybrid Fixed Point Theorems and Their Applications to Fractional Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
H. M. Srivastava ◽  
Sachin V. Bedre ◽  
S. M. Khairnar ◽  
B. S. Desale
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Lower Solution ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Normed Linear Spaces ◽  
Monotonicity Conditions

Some hybrid fixed point theorems of Krasnosel’skii type, which involve product of two operators, are proved in partially ordered normed linear spaces. These hybrid fixed point theorems are then applied to fractional integral equations for proving the existence of solutions under certain monotonicity conditions blending with the existence of the upper or lower solution.

scholarly journals Fixed Point Results via α-Admissibility in Extended Fuzzy Rectangular b-Metric Spaces with Applications to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 2009
Author(s):  
Badshah-e-Rome ◽  
Muhammad Sarwar ◽  
Rosana Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Existence Of Solutions

In this article, the concept of extended fuzzy rectangular b-metric space (EFRbMS, for short) is initiated, and some fixed point results frequently used in the literature are generalized via α-admissibility in the setting of EFRbMS. For the illustration of the work presented, some supporting examples and an application to the existence of solutions for a class of integral equations are also discussed.

scholarly journals On fuzzy Volterra integral equations with deviating arguments

2004 ◽  
Vol 2004 (2) ◽  
pp. 169-176 ◽  
Author(s):  
K. Balachandran ◽  
P. Prakash
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Volterra Integral Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We investigate the problem of existence of solutions of fuzzy Volterra integral equations with deviating arguments. The results are obtained by using the Darbo fixed point theorem.

scholarly journals Generalized contraction mappings of rational type and applications to nonlinear integral equations

2018 ◽  
Vol 38 (1) ◽  
pp. 131-149
Author(s):  
José R. Morales ◽  
Edixon M. Rojas ◽  
Ravindra K. Bisht
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Generalized Contraction ◽  
Nonlinear Integral Equations ◽  
Contraction Mappings ◽  
New Class ◽  
Common Fixed Point Theorems ◽  
Rational Type

The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

scholarly journals SOME COMMON FIXED POINT RESULTS FOR RATIONAL CONTRACTION TYPE VIA THE C-CLASS FUNCTIONS ON METRIC SPACES

2019 ◽  
pp. 231
Author(s):  
Nguyen Thi Thanh Ly ◽  
Nguyen Trung Hieu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Nonlinear Integral Equations ◽  
Contraction Type ◽  
Rational Contraction

The purpose of this paper is to prove some common fixed point results for rational contraction type via the C-class functions on metric spaces. As an application, we study the existence of solutions to the system of nonlinear integral equations.

scholarly journals Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

2021 ◽  
Vol 37 (3) ◽  
pp. 407-416
Author(s):  
SHAHRAM BANAEI ◽  
◽  
VAHID PARVANEH ◽  
MOHAMMAD MURSALEEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Fréchet Space ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Type Integral ◽  
Systems Of Integral Equations

"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."

scholarly journals Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Gaston N’Guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Integral System ◽  
Schauder's Fixed Point Theorem ◽  
Globally Attractive

We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

scholarly journals Common Fixed Point Results for GeneralizedαspContractive Mappings and Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Kastriot Zoto ◽  
Ilir Vardhami
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
General Type ◽  
Existence Of Solutions ◽  
System Of Integral Equations ◽  
Contraction Mappings

A class ofg-αsp-admissible mappings and general typeg-αspcontraction mappings onb-metric-like space are defined. Some fixed point results dealing with such a class of contractions are obtained. The generalized contractions considered in this work cover and unify many particular types of contractions. Finally, we present application to the existence of solutions for a system of integral equations by means ofb-metric-like spaces.

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