• Korean Journal of Mathematics
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• 제29권2호
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.295-309
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• 2023

In this paper, we introduce the notion of α-Geraghty contractive type covariant and contravariant mappings in the bipolar metric spaces. In addition, we prove some fixed point theorems, which give existence and uniqueness of fixed point, for α-Geraghty contractive type covariant and contravariant mappings in complete bipolar metric spaces. Finally, we show some examples to support our main results.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.703-717
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• 2023

In this paper, we will introduce the notion of 𝜓-type and Jaggi type hybrid contraction in a bipolar metric space and show the existence and uniqueness of fixed point for such type of contractions. In the end, we will provide some corollaries and support our theorems by examples.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1097-1113
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• 2023

In this paper, we extend some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Hardy-Roger type mappings. Our result generalizes many known results in fixed point theory. Finally, we offer a example to illustrate our result.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.487-499
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• 2024

The main motivation for this paper is to investigate the fixed point property for nonlinear contraction defined on b-Menger inner product spaces. First, we introduce a b-Menger inner product spaces, then the topological structure is discussed and the probabilistic Pythagorean theorem is given and established. Also we prove the existence and uniqueness of fixed point in these spaces. This result generalizes and improves many previously known results.

• Journal of Applied and Pure Mathematics
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• 제6권1_2호
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.61-73
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• 2008

In this paper common fixed point theorems dealing with compatible mappings of type (P) are established. As a application, the existence and uniqueness of common solution for a system of functional equations arising in dynamic programming is given. The results presented in this paper improve, generalize and unify the corresponding results in this field.

• 대한수학회보
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• 제52권3호
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• pp.789-807
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• 2015

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

• 대한수학회보
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• 제47권2호
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• pp.263-274
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• 2010

In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.

• 대한수학회보
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• 제47권2호
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• pp.319-339
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• 2010

In this paper, we prove that if $f^nf'\;-\;P$ and $g^ng'\;-\;P$ share 0 CM, where f and g are two distinct transcendental meromorphic functions, $n\;{\geq}\;11$ is a positive integer, and P is a nonzero polynomial such that its degree ${\gamma}p\;{\leq}\;11$, then either $f\;=\;c_1e^{cQ}$ and $g\;=\;c_2e^{-cQ}$, where $c_1$, $c_2$ and c are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2\;=\;-1$, Q is a polynomial such that $Q\;=\;\int_o^z\;P(\eta)d{\eta}$, or f = tg for a complex number t such that $t^{n+1}\;=\;1$. The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.