Strong convergence of an iterative method for pseudo-contractive and monotone mappings

In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive mapping and solutions of variational inequality problem for monotone mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive mappings and solutions set of finite family of variational inequality problems for continuous monotone mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.     

Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings

In this paper, we prove strong convergence theorems to a zero of monotone mapping and a fixed point of relatively weak nonexpansive mapping. Moreover, strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive mapping and a solution of a certain variational problem are proved under appropriate conditions.     

Fixed point theorems in new generalized metric spaces

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi: 10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler–Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.     

Random fixed points of pseudo-contractive random operators

The paper presents new random fixed point results for pseudo-contractive random operators.     

Synthesis of hexacyclic fused isocoumarin framework through selective domino multicyclizations under catalyst and solvent free conditions

A novel fused isocoumarin skeleton has been synthesized through selective domino multicyclizations by mixing homothallic acid and 2,3-diphenylacryloyl chloride at 200℃ under catalyst and solvent free reaction conditions. Six fused rings with two stereogenic centers were assembled in a convenient onepot operation in good yield. The resulting hexacyclic fused isocoumarin skeleton and its stereochemistry was fully characterized and unambiguously confirmed by X-ray diffraction analysis.     

Evaluation of in vivo hypoglycemic potential of 4-ethyloxychalcone in alloxan-induced diabetic rats

The presently available therapies for type 2 diabetes have not been able to achieve normoglycemic status in a majority of the patients which may be either due to the limitations of the drug itself or its side effects. In an effort to develop potent and safe oral antidiabetic agents, 4-ethyloxychalcone, which was found to be the most potent antiglycating agent in our previous study, has been evaluated for its in vivo hypoglycemic activity using an alloxanized diabetic rat model. The diabetes was induced in rats by injection of intraperitoneal alloxan. However, the oral route was used for the administration of 4-ethyloxychalcone. A significant glucose-lowering effect (P < 0.05) comparable with the standard glibenclamide has been observed for 4-ethyloxychalcone in an oral glucose tolerance test. 4-Ethyloxychalcone also produced a significant decrease (P < 0.05) in fasting blood glucose levels during the 42 days of treatment. Furthermore, a significant lowering (P < 0.05) of glycated hemoglobin (HbA_1C ) level was also shown by 4-ethyloxychalcone after 42 days of treatment. Thus, 4-ethyloxychalcone might be regarded as a potential hypoglycemic agent that can act as a platform for the development of future antidiabetic drugs.     

Synthesis,Crystal Structure and DNA Interaction Study of 3-(2-(3,5-Diphenyl-4,5-dihydropyrazol1-yl)thiazol-4-yl)-2H-chromen-2-one

A new compound 3-(2-(3,5-diphenyl-4,5-dihydropyrazol-1-yl)thiazol-4-yl)-2Hchromen-2-one was synthesized by cyclocondensation of 3,5-diphenyl-4,5-dihydropyrazole-1-carbothioamide with 3-(2-bromoacetyl)-2H-chromen-2-one in ethanol at reflux for 2hrs. The compound was characterized by IR, 1H-NMR, 13C-NMR and single-crystal X-ray diffraction analysis. The newly synthesized compound(C27H19N3O2S) crystallizes in the triclinic system, space group P1 with a = 5.2476(6), b = 18.289(2), c = 23.115(3) , α = 93.546(7), β = 94.715(6), γ = 92.347(7)°, V = 2204.3(4)3, Z = 4, Mr = 449.51, crystal size = 0.38 mm × 0.22 mm × 0.16 mm,(I 2σ(I)) = 35317, 9736, 3785, Rint = 0.081,(Δρ)max = 0.19 and(Δρ)min = –0.24 e·-3. DNA interaction studies revealed that the target compound strongly interacts with DNA through an intercalation binding mode and the binding constant of the compound is 7.45 × 104 M-1.     

Canonical forms of Nielsen's and Cenov's dynamical equations

In this paper, with Poincaré's formalism, and an indirect method, the canonical forms of the generalized equations of motion due to Nielsen and Cenov of a holonomic dynamical system in the velocity-phase space and the acceleration-phase space are obtained in terms of the Poincaré parameters This paper was presented at the International Congress of Mathematicians (ICM), 21–29 August, 1990, Kyoto University, Japan.