Suzuki Type Research Articles

A Suzuki Type Coupled Fixed Point Theorem for Generalized Multivalued Mapping

We obtain a new Suzuki type coupled fixed point theorem for a multivalued mappingTfromX×XintoCB(X), satisfying a generalized contraction condition in a complete metric space. Our result unifies and generalizes various known comparable results in the literature. We also give an application to certain functional equations arising in dynamic programming.

Implicit contractive mappings in modular metric and fuzzy metric spaces.

The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

Discussions on Recent Results forα-ψ-Contractive Mappings

We establish certain fixed point results forα-η-generalized convex contractions,α-η-weakly Zamfirescu mappings, andα-η-Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

Fixed Point Theory inα-Complete Metric Spaces with Applications

The aim of this paper is to introduce new concepts ofα-η-complete metric space andα-η-continuous function and establish fixed point results for modifiedα-η-ψ-rational contraction mappings inα-η-complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems forψ-graphic-rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

A route to the 9,10-secosteroid astrogorgiadiol featuring a key sp2–sp3 Suzuki type cross-coupling

The described semi-synthetic route differs from the previously published approaches by an original C-7–C-8 disconnection. The kinetic enol triflate of Grundmann ketone was chosen as the CD-ring platform on which to couple an A-ring synthon via a challenging sp2–sp3 cross-coupling. A range of A-ring synthons was synthesized to allow the investigations of various conditions of metal-catalyzed couplings. Suzuki-type chemistry provided a useful (89% yield) answer. Whereas the last step of the designed route—a regioselective opening of the epoxide obtained from the alkene, product of the coupling reaction—proved more challenging than expected, a hydroboration endgame route completed a formal synthesis of (−)-astrogorgiadiol.

A Suzuki type unique common fixed point theorem for hybrid pairs of maps under a new condition in partial metric spaces

Abstract In this paper, we introduce a new condition namely, the (W.C.C) condition and give some Suzuki-type, unique, common fixed-point theorems for pairs of hybrid mappings in partial metric spaces using a partial Hausdorff metric. These results generalize and extend the several comparable results in this literature in metric and partial metric spaces.

Some generalizations of Suzuki and Edelstein type theorems

We prove some generalizations of Suzuki’s fixed point theorem and Edelstein’s theorem. MSC:54H25.

Suzuki type fixed point theorems for generalized multi-valued mappings in b-metric spaces

In this paper, we obtained a new condition for a multi-valued mapping in a b-metric space, which guarantees the existence of its fixed point.MSC:47H10, 54H25, 54E50.

Common fixed points for self mappings on compact metric spaces

In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.

A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces

In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming.

Palladium mediated C–H bond activation of thiosemicarbazones: Catalytic application of organopalladium complexes in C–C and C–N coupling reactions

Upon reaction with Pd(PPh3)2Cl2 benzaldehyde thiosemicarbazone undergoes a geometrical change around the imine bond and affords a mixed-ligand complex 1, incorporating an NS-coordinated thiosemicarbazone, a triphenylphosphine and a chloride. Similar reactions with benzophenone thiosemicarbazone and acetophenone thiosemicarbazone proceed without any geometrical change to afford complexes 2 and 3 respectively, containing a CNS-coordinated thiosemicarbazone and a triphenylphosphine. Crystal structures of complexes 1, 2 and 3 have been determined. All the complexes display intense absorptions in the visible region. Catalytic activity of complexes 1, 2 and 3 toward Suzuki type C–C coupling reactions has been examined, and all three are found to efficiently activate all types of C–X bonds (X = I, Br, Cl and even F) and bring about the C–C bond formation with high yield. These complexes are also found to catalyze C–N coupling reactions between aryl halides and primary or secondary amines. While all three complexes are found to be efficient catalysts for both C–C and C–N coupling reactions, complex 2 is found to be a better catalyst than the other two complexes.

New existence theorems for quasi-equilibrium problems and a minimax theorem on complete metric spaces

Motivated by the Suzuki's type fixed point theorems, we give several new existence theorems for scalar quasi-equilibrium problems, and vector quasi-equilibrium problem on complete metric spaces. We give important examples for our results. Note that the solution of quasi-equilibrium problem (resp. vector quasi-equilibrium problem) is unique under suitable conditions, and we can find the unique solution by the Picard iteration. Besides, we also give a new coincidence theorem on complete metric spaces. Finally, we give a new minimax theorem on complete metric spaces. Note that the solution of minimax theorem is unique under suitable conditions, and we can find the unique solution by the Picard iteration.

Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics

In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived.

A new type of contractive multivalued operators

The aim of this paper is to introduce a new type of multivalued operators similar to those of Kikkawa–Suzuki type and to present some basic problems of the fixed point and strict fixed point for them. Obtained results generalize, complement and extend classical results given by Ćirić [Lj.B. Ćirić, Fixed points for generalized multi-valued contractions, Mat. Vesnik 9 (24) (1972) 265–272] or Nadler [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475–488], as well as recent results given by Kikkawa and Suzuki [M. Kikkawa, T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008) 2942–2949], Moţ and Petruşel [G. Moţ, A. Petruşel, Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal. 70 (2009) 3371–3377]. Applications to certain functional equations arising in dynamic programming are also considered.

Routes to synthesis of porphyrins covalently bound to poly(carbazole)s and poly(fluorene)s: Structural and computational studies on oligomers

We report the synthesis, spectroscopic and computational characterization of carbazole and fluorene oligomers containing pendant porphyrins prepared through Suzuki type coupling reactions. Molecular modeling, combining ab initio and semiempirical PM6 methods, has been carried out to clarify the structural geometry of these oligomers, testing the viability of development of polymers with the above repeat units. Based on the above results, and attempts to polymerize these systems, indications are made of possible routes to synthesize poly(carbazole)s and poly(fluorene)s containing covalently bound porphyrins.

The locally 2-arc transitive graphs admitting an almost simple group of Suzuki type

In this paper, seven families of vertex-intransitive locally (G,2)-arc transitive graphs are constructed, where Sz(q)⩽G⩽Aut(Sz(q)), q=22k+1 for some k∈N. It is then shown that for any graph Γ in one of these families, Sz(q)⩽Aut(Γ)⩽Aut(Sz(q)) and that the only locally 2-arc transitive graphs admitting an almost simple group of Suzuki type whose vertices all have valency at least three are (i) graphs in these seven families, (ii) (vertex transitive) 2-arc transitive graphs admitting an almost simple group of Suzuki type, or (iii) double covers of the graphs in (ii). Since the graphs in (ii) have been classified by Fang and Praeger (1999) [6], this completes the classification of locally 2-arc transitive graphs admitting a Suzuki simple group

Some generalizations of Caristi type fixed point theorem on partial metric spaces

In the persent paper, we give Bae and Suzuki type generalizations of Caristi?s fixed point theorem on partial metric space.

Copper(II)‐Mediated Intramolecular Cyclization of (Z)‐Chalcogenoenynes: Synthesis of 3‐Halochalcogenophene Derivatives

AbstractWe present our results on the cyclization of (Z)‐chalcogenoenynes mediated by copper(II) salts to afford 3‐halochalcogenophenes in satisfactory yields through an intramolecular 5‐endo‐dig cyclization. The methodology was carried out using CuCl2 at 50 °C or CuBr2 at room temperature under an ambient atmosphere. The reaction took place under very mild reaction conditions and tolerated considerable functionality. One 3‐bromo‐selenophene derivative was applied as a substrate in the palladium‐catalyzed cross‐coupling reaction with a boronic acid to give the Suzuki type product in good yield.

Synthesis and biological evaluation of new 3-(6-hydroxyindol-2-yl)-5-(Phenyl) pyridine or pyrazine V-Shaped molecules as kinase inhibitors and cytotoxic agents

We here report the synthesis and biological evaluation of new 3-[(2-indolyl)]-5-phenyl-3,5-pyridine, 3-[(2-indolyl)]-5-phenyl-2,4-pyridine and 3-[(2-indolyl)]-5-phenyl-2,6-pyrazine derivatives designed as potential CDK inhibitors. Indoles and phenyls were used to generate several substitutions of the pyridine and pyrazine rings. The synthesis included Stille or Suzuki type reactions, which were carried out on the 3,5-dibromopyridine, 2,4-dichloropyridine and 2,6-dichloro-1-4-pyrazine moieties. Cell effects of the V-shaped family were in the micromolar range. Kinase assays were conducted and showed that compound 11 inhibited CDK5 with an inhibitory concentration of 160 nM with a moderate selectivity over GSK3 compared to the reference C which exhibited a slightly lower activity on CDK5 (1.5 μM). Compound 11 was also found to be the most potent compound in the series and was identified as a new lead for DYRK1A inhibitor discovery (IC50 = 60 nM). Docking studies were carried out in order to investigate the inhibition of DYRK1A.

Copper(I) complexes of N-(aryl)pyridine-2-aldimines: Spectral, electrochemical and catalytic properties

The reactions of N-(aryl)pyridine-2-aldimines ( L– R; R = OCH 3, CH 3, H, Cl and NO 2), derived from pyridine-2-aldehyde and para-substituted anilines, with CuI in methanol under ambient conditions afford a series of brown complexes of the type [{Cu(L–R)I} 2]. The structure of the [{Cu(L–OCH 3)I} 2] complex has been determined by X-ray crystallography. In these dimeric complexes the two copper centers are linked through an iodo-bridge, and the L– R ligands are coordinated to the metal center through the pyridine-nitrogen and imine-nitrogen. All the complexes show characteristic 1H NMR signals and intense MLCT transitions in the visible region. These complexes also show an emission near 465 nm, whilst they are excited at 340 nm, with relatively poor quantum yields ( φ ∼0.002 at 298 K). Cyclic voltammetry on all the complexes shows two successive Cu(I)–Cu(II) oxidations on the positive side of SCE, and a reduction of the coordinated imine ligand on the negative side. These copper(I) complexes are found to efficiently catalyze Suzuki type C–C coupling reactions.