• Title/Summary/Keyword: p-uniformly convex

Search Result 28, Processing Time 0.024 seconds

HYPERGEOMETRIC DISTRIBUTION SERIES AND ITS APPLICATION OF CERTAIN CLASS OF ANALYTIC FUNCTIONS BASED ON SPECIAL FUNCTIONS

  • Murugusundaramoorthy, Gangadharan;Porwal, Saurabh
    • Communications of the Korean Mathematical Society
    • /
    • v.36 no.4
    • /
    • pp.671-684
    • /
    • 2021
  • The tenacity of the current paper is to find connections between various subclasses of analytic univalent functions by applying certain convolution operator involving generalized hypergeometric distribution series. To be more specific, we examine such connections with the classes of analytic univalent functions k - 𝓤𝓒𝓥* (𝛽), k - 𝓢*p (𝛽), 𝓡 (𝛽), 𝓡𝜏 (A, B), k - 𝓟𝓤𝓒𝓥* (𝛽) and k - 𝓟𝓢*p (𝛽) in the open unit disc 𝕌.

SOME RESULTS ON BEST PROXIMITY POINT FOR CYCLIC B-CONTRACTION AND S-WEAKLY CYCLIC B-CONTRACTION MAPPINGS

  • V. Anbukkarasi ;R. Theivaraman;M. Marudai ;P. S. Srinivasan
    • The Pure and Applied Mathematics
    • /
    • v.30 no.4
    • /
    • pp.417-427
    • /
    • 2023
  • The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

FIXED POINTS OF A CERTAIN CLASS OF ASYMPTOTICALLY REGULAR MAPPINGS

  • Jung, Jong-Soo;Thakur, Balwant-Singh;Sahu, Daya-Ram
    • Bulletin of the Korean Mathematical Society
    • /
    • v.37 no.4
    • /
    • pp.729-741
    • /
    • 2000
  • In this paper, we study in Banach spaces the existence of fixed points of asymptotically regular mapping T satisfying: for each x, y in the domain and for n=1, 2,…, $$\parallelT^nx-T^ny\parallel\leq$\leq$a_n\parallelx-y\parallel+b_n (\parallelx-T^nx\parallel+\parallely-T^ny\parallely)$$ where $a_n,\; b_n,\; C_n$ are nonnegative constants satisfying certain conditions. We also establish some fixed point theorems for these mappings in a Hibert space, in L(sup)p spaces, in Hardy space H(sup)p, and in Soboleve space $H^{k,p} for 1<\rho<\infty \; and \; k\geq0$. We extend results from papers [10], [11], and others.

  • PDF

PROXIMITY MAPS FOR CERTAIN SPACES

  • Lee, Mun-Bae;Park, Sung-Ho
    • Bulletin of the Korean Mathematical Society
    • /
    • v.34 no.2
    • /
    • pp.259-271
    • /
    • 1997
  • Let K be a nonempty subset of a normed linear space X and let x $\in$ X. An element k$_0$ in K satisfying $\$\mid$$x - k$_0$$\$\mid$$ = d(x, K) := (equation omitted) $\$\mid$$x - k$\$\mid$$ is called a best approximation to x from K. For any x $\in$ X, the set of all best approximations to x from K is denoted by P$_K$(x) = {k $\in$ K : $\$\mid$$ x - k $\$\mid$$ = d(x, K)}. (omitted)

  • PDF

NEW HYBRID ALGORITHM FOR WEAK RELATIVELY NONEXPANSIVE MAPPING AND INVERSE-STRONGLY MONOTONE MAPPING IN BANACH SPACE

  • Zhang, Xin;Su, Yongfu;Kang, Jinlong
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.1_2
    • /
    • pp.87-102
    • /
    • 2011
  • The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

STRONG CONVERGENCE THEOREMS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY-MONOTONE MAPPINGS IN A BANACH SPACE

  • Liu, Ying
    • East Asian mathematical journal
    • /
    • v.26 no.5
    • /
    • pp.627-639
    • /
    • 2010
  • In this paper, we introduce a new iterative sequence finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly-monotone mapping, the fixed point problem and the classical variational inequality problem. Our results improve and extend the corresponding results announced by many others.

SURFACE CHARACTERISTICS AND BIOACTIVITY OF ANODICALLY OXIDIZED TITANIUM SURFACES (양극산화에 의한 티타늄 산화막의 표면 특성 및 생체 활성에 관한 연구)

  • Lee, Sang-Han;Cho, In-Ho
    • The Journal of Korean Academy of Prosthodontics
    • /
    • v.45 no.1
    • /
    • pp.85-97
    • /
    • 2007
  • Statement of problem: Recently, anodic oxidation of cp-titanium is a popular method for treatment of titanium implant surfaces. It is a relatively easy process, and the thickness, structure, composition, and the microstructure of the oxide layer can be variably modified. Moreover the biological properties of the oxide layer can be controlled. Purpose: In this study, the roughness, microstructure, crystal structure of the variously treated groups (current, voltage, frequency, electrolyte, thermal treatment) were evaluated. And the specimens were soaked in simulated body fluid (SBF) to evaluate the effects of the surface characteristics and the oxide layers on the bioactivity of the specimens which were directly related to bone formation and integration. Materials and methods: Surface treatments consisted of either anodization or anodization followed thermal treatment. Specimens were divided into seven groups, depending on their anodizing treatment conditions: constant current mode (350V for group 2), constant voltage mode (155V for group 3), 60 Hz pulse series (230V for group 4, 300V for group 5), and 1000 Hz pulse series (400V for group 6, 460V for group 7). Non-treated native surfaces were used as controls (group 1). In addition, for the purpose of evaluating the effects of thermal treatment, each group was heat treated by elevating the temperature by $5^{\circ}C$ per minute until $600^{\circ}C$ for 1 hour, and then bench cured. Using scanning electron microscope (SEM), porous oxide layers were observed on treated surfaces. The crystal structures and phases of titania were identified by thin-film x-ray diffractmeter (TF-XRD). Atomic force microscope (AFM) was used for roughness measurement (Sa, Sq). To evaluate bioactivity of modified titanium surfaces, each group was soaked in SBF for 168 hours (1 week), and then changed surface characteristics were analyzed by SEM and TF-XRD. Results: On basis of our findings, we concluded the following results. 1. Most groups showed morphologically porous structures. Except group 2, all groups showed fine to coarse convex structures, and the groups with superior quantity of oxide products showed superior morphology. 2. As a result of combined anodization and thermal treatment, there were no effects on composition of crystalline structure. But, heat treatment influenced the quantity of formation of the oxide products (rutile / anatase). 3. Roughness decreased in the order of groups 7,5,2,3,6,4,1 and there was statistical difference between group 7 and the others (p<0.05), but group 7 did not show any bioactivity within a week. 4. In groups that implanted ions (Ca/P) on the oxide layer through current and voltage control, showed superior morphology, and oxide products, but did not express any bioactivity within a week. 5. In group 3, the oxide layer was uniformly organized with rutile, with almost no titanium peak. And there were abnormally more [101] orientations of rutile crystalline structure, and bonelike apatite formation could be seen around these crystalline structures. Conclusion: As a result of control of various factors in anodization (current, voltage, frequency, electrolytes, thermal treatment), the surface morphology, micro-porosity, the 2nd phase formation, crystalline structure, thickness of the oxide layer could be modified. And even more, the bioactivity of the specimens in vitro could be induced. Thus anodic oxidation can be considered as an excellent surface treatment method that will able to not only control the physical properties but enhance the biological characteristics of the oxide layer. Furthermore, it is recommended in near future animal research to prove these results.