There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Fractional Differential Equations

Theory of fuzzy integrals and its applications

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

In this paper a suboptimization procedure is formulated for Volterra-type equations by using the Kalman-Bucy filtering theory. The Volterra-type systems are, in general, of a time-varying and non-convolution nature, but we include the time-invariant and convolution cases

Kalman-Bucy filtering for stochastic Volterra models

1Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia 2Department of Mathematical Sciences, UAEU, P.O. Box 15551, Al-Ain, UAE 3Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran 4Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, Barrio Sarriena, P.O. Box 644 de Bilbao, Leioa, 48940 Bizkaia, Spain

/pdf/nonlinear-operators-in-fixed-point-theory-with-applications-3957vlkgm0.pdf

Nonlinear Operators in Fixed Point Theory with Applications to Fractional Differential and Integral Equations

The main purpose of the present paper is to define the concept of an e-distance (as a generalization of r-distance) on a Menger PGM space and to introduce some of its properties. Moreover, some coupled fixed point results, in terms of this distance on a complete PGM space, are proved. To support our definitions and main results, several examples and an application are considered.

https://www.mdpi.com/2075-1680/10/1/3/pdf

e-Distance in Menger PGM Spaces with an Application

In this article, we study the Agarwal iterative process for finding fixed points and best proximity points of relatively nonexpansive mappings. Using the Von Neumann sequence, we establish the convergence result in a Hilbert space framework. We present a new example of relatively nonexpansive mapping and prove that its Agarwal iterative process is more efficient than the Mann and Ishikawa iterative processes.

/pdf/approximation-of-fixed-points-and-best-proximity-points-of-2cbc7o8dbm.pdf

Manuel De la Sen

Papers

Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Kalman-Bucy filtering for stochastic Volterra models

Nonlinear Operators in Fixed Point Theory with Applications to Fractional Differential and Integral Equations

e-Distance in Menger PGM Spaces with an Application

Approximation of Fixed Points and Best Proximity Points of Relatively Nonexpansive Mappings