scholarly journals A new perspective for multivalued weakly Picard operators

2017 ◽  
Vol 101 (115) ◽  
pp. 197-204 ◽  
Author(s):  
Gonca Durmaz ◽  
Ishak Altun
Keyword(s):  
Metric Spaces ◽  
Almost Contraction ◽  
Complete Metric Spaces ◽  
Multivalued Contraction ◽  
Recent Developments ◽  
New Perspective

This research contains some recent developments about multivalued weakly Picard operators on complete metric spaces. In addition, taking into account both multivalued ?-contraction and almost contraction on complete metric spaces, we present a new perspective for multivalued weakly Picard operators. Finally, we give a nontrivial example showing that the investigation of this paper is significant.

scholarly journals Coupled Coincidence Point Theorems for New Types of Mixed Monotone Multivalued Mappings in Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chalongchai Klanarong ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Point Theory ◽  
Multivalued Mappings ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Coupled Common Fixed Point ◽  
Recent Developments

We introduce and study new types of mixed monotone multivalued mappings in partially ordered complete metric spaces. We give relationships between those two types of mappings and prove their coupled fixed point and coupled common fixed point theorems in partially ordered complete metric spaces. Some examples of each type of mappings satisfying the conditions of the main theorems are also given. Our main result includes several recent developments in fixed point theory of mixed monotone multivalued mappings.

scholarly journals αH-ψH-Multivalued Contractive Mappings and Related Results in Complete Metric Spaces with An Application

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 68
Author(s):  
Pooja Dhawan ◽  
Kapil Jain ◽  
Jatinderdeep Kaur
Keyword(s):  
Fixed Point ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Contraction ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Homotopy Result

In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application.

scholarly journals Fixed points of Suzuki-type generalized multivalued (f,θ,L)- almost contractions with applications

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 499-518 ◽  
Author(s):  
Naeem Saleem ◽  
Mujahid Abbas ◽  
Basit Ali ◽  
Zahid Raza
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Frame Work ◽  
Proper Generalization

In this paper, we define Suzuki type generalized multivalued almost contraction mappings and prove some related fixed point results. As an application, some coincidence and common fixed point results are obtained. The results proved herein extend the recent results on fixed points of Kikkawa Suzuki type and almost contraction mappings in the frame work of complete metric spaces. We provide examples to show that obtained results are proper generalization of comparable results in the existing literature. Some applications in homotopy, dynamic programming, integral equations and data dependence problems are also presented.

scholarly journals Fixed point theorems for Presic almost contraction mappings in orbitally complete metric spaces endowed with directed graphs

2016 ◽  
Vol 32 (3) ◽  
pp. 303-313
Author(s):  
PORNPIMON BORIWAN ◽  
◽  
NARIN PETROT ◽  
SUTHEP SUANTAI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Directed Graphs ◽  
Product Spaces ◽  
Almost Contraction ◽  
Contraction Mappings ◽  
Complete Metric Spaces

The main aim of this paper is to introduce a class of generalized contractions in product spaces in the sense of Presiˇ c. Some examples and fixed point theorems for such introduced mappings in the setting of orbitally ´ complete metric spaces are proved. The results presented here extend and include many existing several results in the literature.

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

A generalization of Reich’s fixed point theorem for multi-valued mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3295-3305 ◽  
Author(s):  
Antonella Nastasi ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Motivated by a problem concerning multi-valued mappings posed by Reich [S. Reich, Some fixed point problems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 57 (1974) 194-198] and a paper of Jleli and Samet [M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014) 1-8], we consider a new class of multi-valued mappings that satisfy a ?-contractive condition in complete metric spaces and prove some fixed point theorems. These results generalize Reich?s and Mizoguchi-Takahashi?s fixed point theorems. Some examples are given to show the usability of the obtained results.

scholarly journals On Some New Contractive Conditions in Complete Metric Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Jelena Vujaković ◽  
Eugen Ljajko ◽  
Mirjana Pavlović ◽  
Stojan Radenović
Keyword(s):  
Current Literature ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Nonlinear Anal ◽  
Increasing Mapping ◽  
Strictly Increasing Mapping

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F:(0,+∞)→(−∞,+∞). According to the recently obtained results, this was possible (Wardowski’s method) only if two more properties (F2) and (F3) were used instead of the aforementioned strictly increasing (F1). Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α(u,v)=1 for every u and v from metric space Ξ, we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained.

scholarly journals Multivalued weak cyclic δ-contraction mappings

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pulak Konar ◽  
Samir Kumar Bhandari ◽  
Sumit Chandok ◽  
Aiman Mukheimer
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Cyclic Contraction ◽  
Contraction Mappings ◽  
Multivalued Contraction ◽  
New Type

AbstractIn this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

scholarly journals Discussions on the almost 𝒵-contraction

2020 ◽  
Vol 18 (1) ◽  
pp. 448-457
Author(s):  
Erdal Karapınar ◽  
V. M. L. Hima Bindu
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
The Given

Abstract In this paper, we introduce a new contraction, namely, almost {\mathcal{Z}} contraction with respect to \zeta \in {\mathcal{Z}} , in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.

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