A Fixed Point Theorem for Elliptic Complexes

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.

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Investigation of the neutral fractional differential inclusions of Katugampola-type involving both retarded and advanced arguments via Kuratowski MNC technique

Advances in Difference Equations ◽

10.1186/s13662-021-03377-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sina Etemad ◽

Mohammed Said Souid ◽

Benoumran Telli ◽

Mohammed K. A. Kaabar ◽

Shahram Rezapour

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Differential Inclusions ◽

Measure Of Noncompactness ◽

Research Work ◽

Neutral System ◽

Fractional Differential Inclusions ◽

Kuratowski Measure Of Noncompactness ◽

Fractional Differential

AbstractA class of the boundary value problem is investigated in this research work to prove the existence of solutions for the neutral fractional differential inclusions of Katugampola fractional derivative which involves retarded and advanced arguments. New results are obtained in this paper based on the Kuratowski measure of noncompactness for the suggested inclusion neutral system for the first time. On the one hand, this research concerns the set-valued analogue of Mönch fixed point theorem combined with the measure of noncompactness technique in which the right-hand side is convex valued. On the other hand, the nonconvex case is discussed via Covitz and Nadler fixed point theorem. An illustrative example is provided to apply and validate our obtained results.

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Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations

Advances in Difference Equations ◽

10.1186/s13662-020-02703-z ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Vahid Parvaneh ◽

Maryam Khorshidi ◽

Manuel De La Sen ◽

Hüseyin Işık ◽

Mohammad Mursaleen

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Integral Equations ◽

Point Theorem ◽

Measure Of Noncompactness ◽

System Of Integral Equations ◽

Darbo’S Fixed Point Theorem

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