0000000000330135
AUTHOR
Hemant Kumar Nashine
On multivalued weakly Picard operators in partial Hausdorff metric spaces
We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.
Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems
1Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, Chhattisgarh 492101, India 2Department of Mathematics and AppliedMathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South Africa 3Departement de Mathematiques et de Statistique, Universite de Montreal, CP 6128, Succursale Centre-Ville, Montreal, QC, Canada H3C 3J7 4Department of Mathematics and Informatics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Coupled coincidence points for compatible mappings satisfying mixed monotone property
We establish coupled coincidence and coupled fixed point results for a pair of mappings satisfying a compatibility hypothesis in partially ordered metric spaces. An example is given to illustrate our obtained results.
Best proximity point theorems for rational proximal contractions
Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.
Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces
Abstract Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. Examples are provided when these results can be applied and neither corresponding metric results nor the results with the standard completeness assumption of the underlying partial metric space can. MSC:47H10, 54H25.
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.
Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations
Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.