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In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is provided to illustrate and support our main results.

We establish three types of nonlinear fixed point theorems in regular semimetric spaces. First, we generalize Miculescu and Mihail’s result, thereby unifying the Matkowski fixed point theorem and the Istrăţescu fixed point theorem concerning convex contractions within the semimetric framework. Second, by introducing a sufficient condition for Cauchy sequences, we prove a fixed point theorem for weak quasicontractions with comparison functions. Third, applying two foundational lemmas, we extend the Boyd‐Wong fixed point theorem to regular semimetric spaces. Our results derive the relevant theorems in metric, b ‐metric, and ultrametric spaces as special cases, which further demonstrates the generalizability of our results.

In this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan’s fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature.

In this article, we introduce several new extensions of Darbo’s fixed point theorem with newly constructed contraction functions associated with the measure of noncompactness. We apply our new extensions to prove the existence of solutions for a system of weighted fractional integral equations in Banach space BC(R+). At the end, we establish an example to show the applicability of our discovery.

We extend Nadler’s fixed point theorem to ν-generalized metric spaces. Through the proof of the above extension, we understand more deeply the mathematical structure of a ν-generalized metric space. In particular, we study the completeness of the space. We also improve Caristi’s and Subrahmanyam’s fixed point theorems in the space.

In this paper, we give new examples to show that the continuity actually strictly stronger than the Fatou property in b-metric spaces. We establish a new fixed point theorem for new essential and fundamental sufficient conditions such that a Ćirić type contraction with contraction constant λ ∈ [ 1 s , 1 ) in a complete b-metric space with s > 1 have a unique fixed point. Many new examples illustrating our results are also given. Our new results extend and improve many recent results and they are completely original and quite different from the well known results on the topic in the literature.

In the current work, the multi-valued version of well-known theorems of Nadler, Banach, Branciari and Reich are generalized to the scope of double controlled metric space. A double controlled metric space is a metric type space in which the right hand side of the triangle inequality is controlled by two functions. Furthermore, applications to existence of solution to Volterra integral inclusions and singular Fredholm integral inclusions of are obtained.

Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions. Our existence results rely on the endpoint theory, the Krasnosel’skiĭ’s fixed point theorem for multivalued maps and Wegrzyk’s fixed point theorem for generalized contractions. We demonstrate the application of the obtained results with the help of examples.

In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of S\\(\\mathcal{S}\\)-asymptotically ω-periodic mild solutions. The applied techniques are supported by the concept of measure of noncompactness in conjunction with the well-known Darbo–Sadovskii and Tichonov fixed-point theorems. Furthermore, an example to the fractional initial/boundary value Cauchy problem is concerned to illustrate our main results.

In this memoir we present proofs of basic results, including those developed so far by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation + 1. A prime end theory is developed through hyperbolic chords in maximal round balls contained in the complement of a non-separating plane continuum We introduce the notion of an oriented map of the plane and show that the perfect oriented maps of the plane coincide with confluent (that is composition of monotone and open) perfect maps of the plane. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982. A continuous map of an interval