Abstract
In this manuscript, we establish two Wardowski–Feng–Liu-type fixed point theorems for orbitally lower semicontinuous functions defined in orbitally complete b-metric spaces. The obtained results generalize and improve several existing theorems in the literature. Moreover, the findings are justified by suitable nontrivial examples. Further, we also discuss ordered version of the obtained results. Finally, an application is presented by using the concept of fractal involving a certain kind of fractal integral equations. An illustrative example is presented to substantiate the applicability of the obtained result in reducing the energy of an antenna.
Highlights
Through the whole of the last century, mathematicians engrossed themselves with touching up the underlying metric framework of the acclaimed Banach contraction principle
We establish two Wardowski–Feng–Liu-type fixed point theorems for orbitally lower semicontinuous functions defined in orbitally complete b-metric spaces
An application is presented by using the concept of fractal involving a certain kind of fractal integral equations
Summary
Through the whole of the last century, mathematicians engrossed themselves with touching up the underlying metric framework of the acclaimed Banach contraction principle. Cosentino et al in [5] introduced the set of functions TFb in the line of Wardowski’s [19] approach to b-metric space as follows: Definition 2. C ∈ (0, 1) with b < c such that for any x ∈ X, there is y ∈ T x satisfying c d(x, y) f (x) and f (y) b d(x, y), T has a fixed point Against this background, we obtain fixed point results for multivalued mappings satisfying Wardowski–Feng–Liu-type conditions for orbitally lower semicontinuous functions in orbitally complete b-metric spaces. We obtain fixed point results for multivalued mappings satisfying Wardowski–Feng–Liu-type conditions for orbitally lower semicontinuous functions in orbitally complete b-metric spaces These results generalize, complement and unify the findings proposed in [2, 12]. An illustrative example is presented to show the applicability of the obtained result in reducing the energy of an antenna
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