Affiliations: [a] Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan
| [b] KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Khru, Bangkok, Thailand
Correspondence:
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Corresponding author. Nayyar Mehmood, Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan. E-mail: [email protected].
Abstract: In this article we introduce the notion of fuzzy measure of noncompactness. We define the fuzzy condensing and fuzzy k-set contractions using fuzzy measure of noncompactness. An extension of Stanislaw Szulfa’s fixed point theorem for a self-operator on a closed bounded and convex subset of a Banach space has been proved. Using the defined multivalued k-set contractions, generalizations of Kakutani-Fan and Krasnoselskii type theorems have been proved. For applications the existence result for solutions of a fractional Caputo-Fabrizio anti-periodic boundary value problem has been proved. We give some examples to validate our results.
