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Displaying similar documents to “Kannan-type cyclic contraction results in 2 -Menger space”

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. Choudhury, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we introduce generalized cyclic contractions through r number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t -norm. In another theorem we use a control function with minimum t -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

On the Rockafellar theorem for Φ γ ( · , · ) -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let Γ : X 2 Φ be a cyclic Φ γ ( · , · ) -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the Φ γ ( · , · ) -subdifferential of f, Γ ( x ) Φ γ ( · , · ) f | x .

Resolving sets of directed Cayley graphs for the direct product of cyclic groups

Demelash Ashagrie Mengesha, Tomáš Vetrík (2019)

Czechoslovak Mathematical Journal

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A directed Cayley graph C ( Γ , X ) is specified by a group Γ and an identity-free generating set X for this group. Vertices of C ( Γ , X ) are elements of Γ and there is a directed edge from the vertex u to the vertex v in C ( Γ , X ) if and only if there is a generator x X such that u x = v . We study graphs C ( Γ , X ) for the direct product Z m × Z n of two cyclic groups Z m and Z n , and the generating set X = { ( 0 , 1 ) , ( 1 , 0 ) , ( 2 , 0 ) , , ( p , 0 ) } . We present resolving sets which yield upper bounds on the metric dimension of these graphs for p = 2 and 3 .

Ramification in quartic cyclic number fields K generated by x 4 + p x 2 + p

Julio Pérez-Hernández, Mario Pineda-Ruelas (2021)

Mathematica Bohemica

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If K is the splitting field of the polynomial f ( x ) = x 4 + p x 2 + p and p is a rational prime of the form 4 + n 2 , we give appropriate generators of K to obtain the explicit factorization of the ideal q 𝒪 K , where q is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

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We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

Bicrossed products of generalized Taft algebra and group algebras

Dingguo Wang, Xiangdong Cheng, Daowei Lu (2022)

Czechoslovak Mathematical Journal

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Let G be a group generated by a set of finite order elements. We prove that any bicrossed product H m , d ( q ) k [ G ] between the generalized Taft algebra H m , d ( q ) and group algebra k [ G ] is actually the smash product H m , d ( q ) k [ G ] . Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of G . As an application, the classification of H m , d ( q ) k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C n denotes the n -cyclic group.

Isometric embeddings of a class of separable metric spaces into Banach spaces

Sophocles K. Mercourakis, Vassiliadis G. Vassiliadis (2018)

Commentationes Mathematicae Universitatis Carolinae

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Let ( M , d ) be a bounded countable metric space and c > 0 a constant, such that d ( x , y ) + d ( y , z ) - d ( x , z ) c , for any pairwise distinct points x , y , z of M . For such metric spaces we prove that they can be isometrically embedded into any Banach space containing an isomorphic copy of .

On almost everywhere differentiability of the metric projection on closed sets in l p ( n ) , 2 < p <

Tord Sjödin (2018)

Czechoslovak Mathematical Journal

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Let F be a closed subset of n and let P ( x ) denote the metric projection (closest point mapping) of x n onto F in l p -norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in n in the Euclidean case p = 2 . We consider the case 2 < p < and prove that the i th component P i ( x ) of P ( x ) is differentiable a.e. if P i ( x ) x i and satisfies Hölder condition of order 1 / ( p - 1 ) if P i ( x ) = x i .