scholarly journals Fractional q-Difference Inclusions in Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 91
Author(s):  
Badr Alqahtani ◽  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Sara Salem Alzaid
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Results ◽  
Infinite Dimensional ◽  
Difference Inclusions

In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch’s fixed point theorems). Finally we give an illustrative example in the last section. We initiate the study of fractional q-difference inclusions on infinite dimensional Banach spaces.

scholarly journals Instantaneous and Noninstantaneous Impulsive Integrodifferential Equations in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Gaston M. N'Guérékata
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
The Resolvent Operator

This paper deals with some existence of mild solutions for two classes of impulsive integrodifferential equations in Banach spaces. Our results are based on the fixed point theory and the concept of measure of noncompactness with the help of the resolvent operator. Two illustrative examples are given in the last section.

scholarly journals Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hernán R. Henríquez ◽  
Marcos Rabelo ◽  
Luciana Vale
Keyword(s):  
Fixed Point ◽  
Differential Inclusions ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Second Order ◽  
Cauchy Problems ◽  
Impulsive Conditions

In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.

scholarly journals Existence of solutions for delay evolution equations with nonlocal conditions

2017 ◽  
Vol 15 (1) ◽  
pp. 616-627 ◽  
Author(s):  
Xuping Zhang ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Existence Results ◽  
Kuratowski Measure Of Noncompactness

Abstract In this paper, we are devoted to study the existence of mild solutions for delay evolution equations with nonlocal conditions. By using tools involving the Kuratowski measure of noncompactness and fixed point theory, we establish some existence results of mild solutions without the assumption of compactness on the associated semigroup. Our results improve and generalize some related conclusions on this issue. Moreover, we present an example to illustrate the application of the main results.

scholarly journals On Milman’s moduli for Banach spaces

2001 ◽  
Vol 6 (2) ◽  
pp. 115-129 ◽  
Author(s):  
Elisabetta Maluta ◽  
Stanislaw Prus ◽  
Mariusz Szczepanik
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniform Convexity ◽  
Infinite Dimensional ◽  
Uniform Smoothness

We show that infinite dimensional geometric moduli introduced by Milman are strongly related to nearly uniform convexity and nearly uniform smoothness. An application of those moduli to fixed point theory is given.

scholarly journals The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Dezhou Kong ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Projection Operator ◽  
Best Approximation ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Projection ◽  
Approximation Theorems ◽  
Generalized Projection Operator

We prove that Fan’s theorem is true for discontinuous increasing mappingsfin a real partially ordered reflexive, strictly convex, and smooth Banach spaceX. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. Moreover, we get some properties of the generalized projection operator in Banach spaces. As applications of our best approximation theorems, the fixed point theorems for non-self-maps are established and proved under some conditions. Our results are generalizations and improvements of the recent results obtained by many authors.

scholarly journals Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Erdal Karapınar ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Fractional Differential ◽  
Implicit Fractional Differential Equations

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Common Fixed Point Theorems for Generalized Cyclic Contraction Pair in Partial B-Metric Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 85-89
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of generalized cyclic contraction pair with transitive mapping in partial b-metric spaces. Also, we establish some fixed point theorems for this contraction pair. Our results generalize and improve the result of Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho (Fixed Point Theory App. 2015:164) in partial-b-metric spaces.

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