Taiwanese Journal of Mathematics

Fixed Point Theorems via MNC in Ordered Banach Space with Application to Fractional Integro-differential Evolution Equations

Hemant Kumar Nashine, He Yang, and Ravi P. Agarwal

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Abstract

In this paper, we propose fixed point results through the notion of measure of noncompactness (MNC) in partially ordered Banach spaces. We also prove some new coupled fixed point results via MNC for more general class of function. To achieve this result, we relaxed the conditions of boundedness, closedness and convexity of the set at the expense that the operator is monotone and bounded. Further, we apply the obtained fixed point theorems to prove the existence of mild solutions for fractional integro-differential evolution equations with nonlocal conditions. At the end, an example is given to illustrate the rationality of the abstract results for fractional parabolic equations.

Article information

Source
Taiwanese J. Math., Volume 22, Number 2 (2018), 421-438.

Dates
Received: 12 January 2017
Revised: 26 June 2017
Accepted: 25 July 2017
First available in Project Euclid: 8 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1504836028

Digital Object Identifier
doi:10.11650/tjm/8198

Mathematical Reviews number (MathSciNet)
MR3780726

Zentralblatt MATH identifier
06965379

Subjects
Primary: 35F25: Initial value problems for nonlinear first-order equations 45N05: Abstract integral equations, integral equations in abstract spaces 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
partially ordered Banach space measure of noncompactness fixed point coupled fixed point fractional integro-differential evolution equation

Citation

Nashine, Hemant Kumar; Yang, He; Agarwal, Ravi P. Fixed Point Theorems via MNC in Ordered Banach Space with Application to Fractional Integro-differential Evolution Equations. Taiwanese J. Math. 22 (2018), no. 2, 421--438. doi:10.11650/tjm/8198. https://projecteuclid.org/euclid.twjm/1504836028


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